For any nonempty set $t$ whose elements are positive integers, define $f(t)$ to be the square of the product of the elements of $t$. for example, if $t=\{1,3,6\}$, then $f(t)=(1\cdot 3\cdot 6)^2 = 18^2 = 324$. consider the nonempty subsets $t$ of $\{1,2,3,4,5,6,7\}$ that do not contain two consecutive integers. if we compute $f(t)$ for each such set, then add up the resulting values, what do we get?

We get

$225+324+441+576+784+1125+2304+3136+4900+11025=24840$

Step-by-step explanation:

$(1\cdot 3\cdot 5)^2 = 15^2 = 225$

$(1\cdot 3\cdot 6)^2 = 18^2 = 324$

$(1\cdot 3\cdot 7)^2 = 21^2 = 441$

$(1\cdot 4\cdot 6)^2 = 24^2 = 576$

$(1\cdot 4\cdot 7)^2 = 28^2 = 784$

$(1\cdot 5\cdot 7)^2 = 35^2 = 1125$

$(2\cdot 4\cdot 6)^2 = 48^2 = 2304$

$(2\cdot 7\cdot 7)^2 = 56^2 = 3136$

$(2\cdot 5\cdot 7)^2 = 70^2 = 4900$

$(3\cdot 5\cdot 7)^2 = 105^2 = 11025$

We get

$225+324+441+576+784+1125+2304+3136+4900+11025=24840$

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

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step-by-step explanation: